Yes there is a couple of modifications for the BKD engine referring to rough idling and misfiring under acceleration.
First one is a change to the installed software and replacement of the PD injectors.
This can only be done using VAS 5052 but also requires a change of injectors to a different part number so is going to be very expensive on a car that is out of warranty.
This mod was only done on cars with a very serious idling
problem though, slight roughness at idle was deemed to be normal !?!?
Also for this engine there is another modification done, mainly to erradicate a misfire when accelerating, usually around 1000 to 1500rpm.
This is much more of a common
problem and seems more to occur on engines with a slightly higher mileage.
There is a new loom for the PD injectors fitted inside the cylinder head , part number 03G 971 033 D.
To check if this has been done you will need to remove the camshaft cover and check the tag on the loom for its part number. If it has anything other than the above number it needs to be replaced as there can be a connection
problem with them.
There are also quite a few checks that need to be done ideally with VCDS(Vag-Com) to determine if bubbling is present in the injectors as there are one or two faults that can crop up in relation to the fuel flow through the head casting into the injectors and injectors coming loose in the head.
Again these will also give the symtoms you describe but are somewhat rarer.
Unfortunately diagnosis of this nature would need to be entrusted to a highly experienced diagostic tech with the correct equipment or a VW Agent.